Luan is not acceptable under any flooring. It tends to have voids between the plys which can collapse. It also can stain. I wouldn't put any vinyl plank directly on the old plank floor either. At the least, I would use an underlayment grade 1/4 plywood subfloor. If it were mine, I would probably put at least 1/2 plywood over the planks.

Thanks for your reply, Floorist. I only mentioned Luan specifically because a friend who almost had LVT installed and had a similar plank subfloor was told by his installer that he wouldn't put in the flooring without first adding a layer of Luan. But what you've said makes sense. My only fear with putting in 1/2 plywood over the planks and then the LVT is that the threshold into the kitchen might look a little silly with such a big step down. If I put in 1/4 plywood will I be unhappy with the final installed results? Should I maybe step up to 3/8 plywood as a happy median?